White House officials and Democrats fanned out to defend President Biden’s mental fitness on Sunday, reflecting the rising anxiety in the president’s administration over a special counsel report that fueled concern about his age.

“This is a report that went off the rails,” Bob Bauer, Mr. Biden’s personal lawyer, said on CBS’s “Face the Nation.” “A shabby work product.”

The report, released on Thursday, cleared Mr. Biden of criminal wrongdoing in his handling of classified documents after leaving the vice presidency. But the special counsel in the case, Robert K. Hur, characterized Mr. Biden, 81, as a “well-meaning, elderly man with a poor memory” who had “diminished faculties in advancing age.”

Democrats have gone on the offensive to discredit what they say is a partisan hit that potentially violated Justice Department policy, specifically taking issue with the descriptions questioning Mr. Biden’s memory.

Alejandro N. Mayorkas, Mr. Biden’s homeland security secretary, said on NBC’s “Meet the Press” that “the responsibility of a federal prosecutor is to investigate and learn the facts and apply the law to those facts.”

“The special counsel did this in the case, made a conclusion that there is no case — case closed — then made gratuitous, unnecessary and inaccurate personal remarks, and those are improper,” Mr. Mayorkas said.

While the report found that “no criminal charges are warranted” against Mr. Biden, the descriptions about his memory put a spotlight on what was already a primary concern for voters: his age. In New York Times/Siena College polling in the fall, more than 70 percent of battleground state voters agreed with the statement that Mr. Biden was “just too old to be an effective president.”

“We have to face the reality of the fact that when you get to those ages, you get diminished,” Nikki Haley, the former South Carolina governor and Republican presidential candidate who has also attacked the mental acuity of former president Donald J. Trump, said on “Face the Nation.” “These are people making decisions on our national security. These are people making decisions on the future of our economy. We need to know they’re at the top of their game.”

Senator Tom Cotton, Republican of Arkansas, said the content of the report was not a surprise.

“Look, there’s no new bombshells about President Biden in this,” he said on “Fox News Sunday.” “The American people have seen for years that he is a man with a failing memory. What this report indicates though is that you have a blatant double standard: If Joe Biden is not going to face criminal charges, then Donald Trump shouldn’t be facing criminal charges either.”

Mr. Biden’s allies have also doubled down on a campaign strategy of framing the election as a choice between Mr. Biden and Mr. Trump, whom they paint as a threat to democracy and who faces charges over his own handling of classified documents. Mr. Trump, 77, recently confused the leaders of Hungary and Turkey, warned that the country was on the verge of World War II and claimed that he defeated Barack Obama instead of Hillary Clinton in the 2016 election.

White House officials were also quick to highlight Mr. Trump’s remarks at a campaign event on Saturday, when he said that while he was president, he told leaders of NATO countries that he would “encourage” Russia “to do whatever the hell they want” to countries that had not paid the money they owed to the military alliance.

“What our nation should focus on is the way that Donald Trump is undermining rule of law, democracy and our safety as a nation,” Senator Chris Coons, Democrat of Delaware, said on ABC’s “This Week” when asked about the special counsel’s report.

But it was clear on Sunday that Mr. Biden’s aides and allies also felt a sense of urgency to attack Mr. Hur’s report and persuade voters concerned over Mr. Biden’s age.

“The actual issue is not going to go away,” Quentin James, a co-founder of the Collective PAC, an organization that aims to elect Black officials, said in an interview. “I think the only way to beat it is again to get out there on the road and campaign really hard. And that’s what we expect from any other candidate, regardless of your age or experience.”

Mitch Landrieu, the co-chair of Mr. Biden’s campaign, said on “Meet the Press” that Mr. Biden had already traveled across the country throughout his presidency to describe his domestic agenda.

“It is this ad hominem attack that questioned the president’s capacity,” Mr. Landrieu said of Mr. Hur’s report. He added: “This guy is tough. He’s smart. He’s on his game.”

The White House has also made a point of dispatching officials with prosecutorial backgrounds to attack the credibility of the report. A day after it was released, Vice President Kamala Harris cited her time as a prosecutor as she described the report as “gratuitous” and “politically motivated.”

Erica L. Green and Karoun Demirjian contributed reporting.